Solve the initial value problem.

$x^2\frac{dy}{dx}=\frac{5x^2-x-2}{(x+1)(y+1)},y(1)=1$

Begin by separating the variables. Choose the correct answer below.

A$.\frac{dy}{dx}=\frac{5x^2-x-2}{x^2(x+1)(y+1)}$

B$.\frac{x^2(x+1)}{5x^2-x-2}dy=\frac{1}{y+1}dx$

C$.(y+1)dy=\frac{5x^2-x-2}{x^2(x+1)}dx$

D$.$ The equation is already separated.

The solution is

$($Type an implicit solution. Type an equation using $x$ and $y$ as the variables.$)$